Area of Regular Polygons — Cumulative exam Answers

A regular heptagon has a radius of approximately 27.87 cm and the length of each side is 24.18 cm.What is the approximate area of the heptagon rounded to the nearest whole number? Recall that a heptagon is a polygon with 7 sides.

UV and RV are secant segments that intersect at point V.

On a coordinate plane, parallelogram H I J K is shown. Point H is at (negative 2, 2), point I is at (4, 3), point J is at (4, negative 2), and point K is at (negative 2, negative 3).

A regular hexagon has an apothem measuring 14 cm and an approximate perimeter of 96 cm.

In the diagram, WZ=.

Arc QVT measures 156°.

In quadrilateral QRST, measures (5x+15)°. Angle TQR measures (4x+3)°.

The angle measures of quadrilateral RSTU are shown.m∠R = (2x)°m∠S = (3x – 35)°m∠T = (x + 35)°

Which statements about the octagon are true? Select two options.

Parallelogram L M N O is shown. Angle N is (2 x) degrees and angle L is (3 x minus 20) degrees.

A regular hexagon is shown.

Triangle S R Q is shown. Angle S R Q is a right angle. An altitude is drawn from point R to point T on side S Q to form a right angle. The length of S T is 9, the length of T Q is 16, and the length of R Q is x.

On a coordinate plane, parallelogram P Q R S is shown. Point P is at (5, 1), point Q is at (6, 4), point R is at (3, 10), and point S is at (2, 7).

Juanita is cutting a piece of construction paper in the shape of a parallelogram. Two opposite sides of the parallelogram have lengths (5n − 6) cm and (3n − 2) cm. A third side measures (2n + 3) cm.What are the lengths of two adjacent sides of the parallelogram?

Which angle measures are correct? Select three options.

Triangle MRN is created when an equilateral triangle is folded in half.

Parallelogram L M N O is shown. Angle L is (x + 40) degrees and angle O is (3 x) degrees.

Circle K is shown. Tangents S T and U T intersect at point T outside of the circle. A line is drawn from point T to point R on the opposite side of the circle. It goes through center point K. Lines are drawn from points S and U to center point K.

Given: RT ≅ TV and ST ≅ TUProve: RSVU is a parallelogram. Statements Reasons1.RT ≅ TV; ST ≅ TU1.given2.∠RTS and ∠VTU are vert. ∠s;∠RTU and ∠VTS are vert. ∠s2.definition of vertical angles3.∠RTS ≅ ∠VTU;∠RTU ≅ ∠VTS3.vertical angles are congruent4.?4.SAS congruency theorem5.∠VRS ≅ ∠RVU; ∠USR ≅ ∠SUV; ∠VRU ≅ ∠RVS; ∠RUS ≅ ∠USV5.CPCTC6.∠VRS and ∠RVU, ∠USR and ∠SUV, ∠VRU and ∠RVS, ∠RUS and ∠USV are each a pair of alternate interior angles6.definition of alternate interior angles7.RS ∥ UV and RU ∥ SV7.converse of the parallelogram diagonal theorem8.RSVU is a parallelogram8.definition of parallelogramWhat is the missing statement in step 4?

On a coordinate plane, square A B C D is shown. Point A is at (3, 4), point B is at (2, negative 2), point C is at (negative 4, negative 1), and point D is at (negative 3, 5).